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Indifference Curves and Budget Constraints Indifference Curves and Budget Constraints Module 12 1

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Define an indifference curve and understand the significance of the slope of an indifference curve. ObjectivesObjectives 2

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Define an indifference curve and understand the significance of the slope of an indifference curve. Define a budget constraint, understand how to graph a budget line, and understand the significance of the slope of the budget line. ObjectivesObjectives 3

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Define an indifference curve and understand the significance of the slope of an indifference curve. Define a budget constraint, understand how to graph a budget line, and understand the significance of the slope of the budget line. Understand how to identify the utility-maximizing bundle and illustrate this graphically. ObjectivesObjectives 4

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Define an indifference curve and understand the significance of the slope of an indifference curve. Define a budget constraint, understand how to graph a budget line, and understand the significance of the slope of the budget line. Understand how to identify the utility-maximizing bundle and illustrate this graphically. Understand how the rule of equal marginal utility per dollar holds at the consumer’s equilibrium bundle. ObjectivesObjectives 5

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Define an indifference curve and understand the significance of the slope of an indifference curve. Define a budget constraint, understand how to graph a budget line, and understand the significance of the slope of the budget line. Understand how to identify the utility-maximizing bundle and illustrate this graphically. Understand how the rule of equal marginal utility per dollar holds at the consumer’s equilibrium bundle. Understand how to derive a demand curve using indifference curves and budget lines. ObjectivesObjectives 6

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Indifference curves are a mechanism for illustrating consumers’ tastes and preferences. Define an indifference curve … Objective 1 7

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Indifference curves are a mechanism for illustrating consumers’ tastes and preferences. Two key assumptions in indifference curve analysis: 1. Consumers are able to rank different bundles of goods. For example, given two bundles of goods, bundle A and bundle B, a consumer is able to say: Bundle A is preferred to bundle B; or Bundle B is preferred to bundle A; or Bundle A is equally preferred to bundle B Define an indifference curve … Objective 1 8

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Indifference curves are a mechanism for illustrating consumers’ tastes and preferences. Two key assumptions in indifference curve analysis: 1. Consumers are able to rank different bundles of goods. For example, given two bundles of goods, bundle A and bundle B, a consumer is able to say: Bundle A is preferred to bundle B; or Bundle B is preferred to bundle A; or Bundle A is equally preferred to bundle B 2.Preferences are transitive. That is, if bundle A is preferred to bundle B and bundle B to bundle C, then bundle A must be preferred to bundle C. Define an indifference curve … Objective 1 9

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In our analysis, we will consider a simple two-good model and only the consumption of goods that are desirable to the consumer as opposed to “undesirables”. Desirable goods are products that give the consumer satisfaction such as movies, clothing, music, etc.. “Undesirables” do not give the consumer satisfaction, for example, pollution. Define an indifference curve … Objective 1 10

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A consumer’s indifference curve shows the various combinations of two goods that give the consumer the same level of utility or satisfaction. Define an indifference curve … Objective 1 11

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A consumer’s indifference curve shows the various combinations of two goods that give the consumer the same level of utility or satisfaction. Define an indifference curve … Objective 1 12 Erin’s indifference curve

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Three properties of indifference curves: Higher indifference curves represent higher levels of satisfaction. Indifference curves … properties … Objective 1 13

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Three properties of indifference curves: Higher indifference curves represent higher levels of satisfaction. Indifference curves are negatively sloped and they are bowed toward the origin. Indifference curves: properties Objective 1 14

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Three properties of indifference curves: Higher indifference curves represent higher levels of satisfaction. Indifference curves are negatively sloped and they are bowed toward the origin. Indifference curves cannot cross. Indifference curves: properties Objective 1 15

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Objective 1: … understand the significance of the slope of an indifference curve An indifference curve is negatively sloped and it is bowed toward the origin (convex). Note that the slope of the indifference curve gets flatter (becomes smaller) as we move down the indifference curve. A convex Indifference curve 16

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Objective 1: … understand the significance of the slope of an indifference curve The slope of an indifference curve tells us the rate at which Erin is willing to trade coffee for an additional bagel with no loss in satisfaction. Slope gets smaller as we move down the indifference 17

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The slope of the indifference curve is referred to as the marginal rate of substitution (MRS). Objective 1: … understand the significance of the slope of an indifference curve 18 Slope gets smaller as we move down the indifference

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The slope of the indifference curve is referred to as the marginal rate of substitution (MRS). The marginal rate of substitution is the rate at which a consumer is willing to give up good Y for an additional unit of good X with no loss in satisfaction. Objective 1: … understand the significance of the slope of an indifference curve 19

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A convex Indifference curve Objective 1: … understand the significance of the slope of an indifference curve 20 The marginal rate of substitution falls as we move down a given indifference curve. Going from point “a” to point “b”, the slope equals 2 ÷ 1 = 2. Going from point “b” to point “c”, the slope equals 1÷2=½. Erin is willing to give up less coffee for each additional bagel, the more bagels she has.

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Key Points: An indifference curve is negatively sloped and it is bowed toward the origin (convex). Objective 1: … understand the significance of the slope of an indifference curve 21

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Key Points: An indifference curve is negatively sloped and it is bowed toward the origin (convex). The slope of an indifference curve measures the consumer’s marginal rate of substitution between two goods. Objective 1: … understand the significance of the slope of an indifference curve 22

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Key Points: An indifference curve is negatively sloped and it is bowed toward the origin (convex). The slope of an indifference curve measures the consumer’s marginal rate of substitution between two goods. The marginal rate of substitution falls as we move down a convex indifference curve. Objective 1: … understand the significance of the slope of an indifference curve 23

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Objective 2 Define a budget constraint … The budget constraint indicates the amount of income a consumer allocates to goods and services. The budget constraint is also called an income constraint. 24

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Objective 2 Define a budget constraint … The budget constraint indicates the amount of income a consumer allocates to goods and services. Suppose Erin has $I to spend on bagels and coffee. Let P b = price of bagels and P c = price of coffee. 25

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Objective 2 Define a budget constraint … The budget constraint indicates the amount of income a consumer allocates to goods and services. Suppose Erin has $I to spend on bagels and coffee. Let P b = price of bagels and P c = price of coffee. We can write an equation for Erin’s budget constraint: Where = Price of bagels × Quantity of bagels = expenditure on bagels, = Price of coffee × Quantity of coffee = expenditure on coffee, and = Price of coffee × Quantity of coffee = expenditure on coffee, and I = income 26

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Suppose Erin has $18 to spend on coffee and bagels. The price of coffee is $3 and the price of bagels is $2. Objective 2: … equation of a budget constraint constraint 27

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Suppose Erin has $18 to spend on coffee and bagels. The price of coffee is $3 and the price of bagels is $2. Let’s plug this information into the equation of her budget constraint: Objective 2: … equation of a budget constraint 28

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Objective 2: How to graph a budget constraint First, find the intercept values: divide the total income by the price of the good in question. 29

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Objective 2: How to graph a budget constraint First find the intercept values: divide the total income by the price of the good in question. Example: Erin has $18 a week and the price of bagels is $2. If she spends all her income ($18) on bagels, she can buy 9 bagels (income ÷ price of bagels = $18÷$2 = 9). This is the X-intercept. 30

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Objective 2: how to graph a budget constraint First find the intercept values: divide the total income by the price of the good in question. Example: Erin has $18 a week and the price of bagels is $2. If she spends all her income ($18) on bagels, she can buy 9 bagels (income ÷ price of bagels = $18÷$2 = 9). This is the X-intercept. The Y-intercept value is (income ÷ price of coffee) $18÷$3 = 6 cups of coffee. 31

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Objective 2: How to graph a budget constraint We can draw Erin’s budget line. Erin can afford all the bundles that lie in the shaded triangle and on its boundaries. The combination of goods on the line exhaust her income of $18. 32

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The slope of the budget line is the negative of the price ratios: Objective 2: … understand the significance of slope of the budget line 33

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Objective 2: … understand the significance of slope of the budget line Y= coffee and X= bagels Slope = rise ÷ run 34

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The slope of the budget line is the negative of the price ratios: − The negative sign indicates that the consumer has to give up some of one good to get more of the other. Objective 2: … understand the significance of slope of the budget line 35

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In our example, the price of bagels = $2 and the price of coffee = $3. Therefore, the slope = −, which means Erin has to give up 2/3 units of coffee to buy 1 additional bagel or 2 units of coffee for 3 additional bagels. Objective 2: … understand the significance of slope of the budget line 36

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The slope of the budget line equals the negative of the price ratio,. The budget line Key Points 37

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The slope of the budget line equals the negative of the price ratio,. The slope indicates how many units of good Y you have to forego to obtain an additional unit of good X. The budget line Key Points 38

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The slope of the budget line equals the negative of the price ratio,. The slope indicates how many units of good Y you have to forego to obtain an additional unit of good X. The ratio of prices is also called the relative prices. The budget line Key Points 39

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The slope of the budget line equals the negative of the price ratio, The slope indicates how many units of good Y you have to forego to obtain an additional unit of good X. The ratio of prices is also called the relative prices. The price ratio is the opportunity cost or the rate of exchange dictated by the market. The budget line Key Points 40

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Objective 3 The equilibrium bundle gives the consumer the highest satisfaction, given her budget constraint. This means that Erin wants to reach the highest indifference curve possible that lie on her budget line. Identify the utility-maximizing combination of goods and illustrate graphically Identify the utility-maximizing combination of goods and illustrate graphically 41

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Objective 3 The equilibrium bundle gives the consumer the highest satisfaction, given her budget constraint. This means that Erin wants to reach the highest indifference curve possible that lie on her budget line. Identify the utility-maximizing combination of goods and illustrate graphically. Identify the utility-maximizing combination of goods and illustrate graphically. Erin’s optimal bundle is “b” which contains 4 cups of coffee and 3 bagels. Her expenditure on this bundle exhausts her income. 42

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At the point of optimal consumption, the indifference curve is tangent to the budget line. Objective 3: … illustratethe utility-maximizing combination of goods and graphically Objective 3: … illustrate the utility-maximizing combination of goods and graphically 43

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Objective 4 Understand how the rule of equal marginal utility per dollar holds in equilibrium 44

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Recall, the optimal consumption bundle (1) exhausts income, and (2) satisfies the rule of equal marginal utility per dollar. Objective 4 Understand how the rule of equal marginal utility per dollar holds in equilibrium 45

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Recall, the optimal consumption bundle (1) exhausts income, and (2) satisfies the rule of equal marginal utility per dollar Since bundle “b” lies on the budget line, the budget is exhausted. Objective 4 Understand how the rule of equal marginal utility per dollar holds in equilibrium 46

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Recall, the optimal consumption bundle (1) exhausts income, and (2) satisfies the rule of equal marginal utility per dollar. Since bundle “b” lies on the budget line, the budget is exhausted. Recall the rule of equal marginal utility per dollar: Objective 4 Understand how the rule of equal marginal utility per dollar holds in equilibrium For the last unit, a dollar spent on bagels yields the same utility as a dollar spent on coffee. 47

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Does bundle “b” satisfy the rule of equal marginal utility per dollar? Understand how the rule of equal marginal utility per dollar holds in equilibrium Objective 4 48

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Does bundle “b” satisfy the rule of equal marginal utility per dollar? Rearrange the equation above to get: ratio of marginal utilities ratio of marginal utilities ratio of prices Understand how the rule of equal marginal utility per dollar holds in equilibrium. Objective 4 49

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The ratio of marginal utilities is the slope of the indifference curve or the marginal rate of substitution Understand how the rule of equal marginal utility per dollar holds in equilibrium Objective 4 50

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The ratio of marginal utilities is the slope of the indifference curve or the marginal rate of substitution The price ratio or relative prices is the slope of the budget line Understand how the rule of equal marginal utility per dollar holds in equilibrium Objective 4 51

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The ratio of marginal utilities is the slope of the indifference curve or the marginal rate of substitution The price ratio or relative prices is the slope of the budget line YES! The rule of equal marginal utility per dollar holds at the point of tangency between the indifference curve and the budget line. Understand how the rule of equal marginal utility per dollar holds in equilibrium. Objective 4 52

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Objective 5 Understand how to derive a demand curve using indifference curves and budget lines 53

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Objective 5 Understand how to derive a demand curve using indifference curves and budget lines The demand curve shows the quantities of a good that a consumer is willing to purchase at alternative prices. 54

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Objective 5 To derive a demand curve using indifference curves and budget lines The demand curve shows the quantities of a good that a consumer is willing to purchase at alternative prices. At a price of $2, Erin’s utility-maximizing choice is 3 bagels. 55

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To derive the demand for bagels curve we must change the price of bagels and observe what happens the quantity demanded, holding all else constant. Suppose the price of bagels falls to $1.50. What happens? Objective 5: … deriving a demand curve 56

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To derive the demand for bagels curve we must change the price of bagels and observe what happens the quantity demanded, holding all else constant. Suppose the price of bagels falls to $1.50. What happens? First, the budget line changes. The new intercept value is 12 bagels (income ÷ new price of bagels = 18 ÷$1.50). The coffee intercept does not change. Objective 5: … deriving a demand curve 57

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What happens to her optimal bundle? Objective 5: … deriving a demand curve 58

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What happens to her optimal bundle? Now, her optimal bundle is bundle “h” containing 4 cups of coffee and 4 bagels. Note, “h” lies on her new budget line. Objective 5: … deriving a demand curve 59

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What happens to her optimal bundle? Now, her optimal bundle is bundle “h” containing 4 cups of coffee and 4 bagels. Note, “h” lies on her new budget line. Thus, when the price of bagels falls from $2.00 to $1.50, Erin increases her quantity demanded from 3 to 4 bagels. Objective 5: … deriving a demand curve 60

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With these two price-quantity combinations, we can derive Erin’s demand for bagels curve Objective 5: … deriving a demand curve 61

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With these two price-quantity combinations, we can derive Erin’s demand for bagels curve Our result is consistent with the law of demand. Objective 5: … deriving a demand curve 62

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Indifference Curves and Budget Constraints Indifference Curves and Budget Constraints End of Module 12 Song:Can’t Buy Me Love Album:Bugs and Friends Sing the Beatles Artists:Bugs Bunny & Daffy Duck 63

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